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Liono4ka [1.6K]
3 years ago
10

Find the sum of all multiples of 4 between 25 and 100​

Mathematics
1 answer:
Mademuasel [1]3 years ago
7 0

Answer:

Sum of all multiples of 4 between 25 and 100 is 1116.

Step-by-step explanation:

Multiples of 4 between 25 and 100 = 28,32,36,40..............,96

let's check the series whether it is an arithmetic progression

a1 = 28 , a2 = 32 , a3 = 36 , a4 = 40

Common difference (d)=a2-a1=32-28 = 4

=a3-a2=36-32 = 4

=a4-a3=40-36 = 4

Common difference exists then the series of numbers is an Arithmetic progression.

To find number of terms :

a(a1) = 28 , d = 4 , l( last term ) = 96

l = a + (n-1)d

96 = 28 + (n-1)4

96 - 28 = (n-1)4

68 = (n-1)4

68/4 = (n-1)

17 = n - 1

17 + 1 = n

18 = n

Sum of all terms:

a = 28 , d = 4 , n = 18 , l = 96

Sn = n/2 ( a + l )

S18 = 18 / 2 (28 + 96)

S18 = 9 (124)

S18 = 1116

Therefore,Sum of all multiples of 4 between 25 and 100 is 1116.

<em>NOTE:</em>

<em>Here </em><em>100 </em><em>is </em><em>also</em><em> </em><em>a </em><em>multiple </em><em>of </em><em>4</em><em> </em><em>but </em><em>question</em><em> </em><em>is </em><em>asked </em><em>between</em><em> </em><em>2</em><em>5</em><em> </em><em>and </em><em>100 </em><em>so </em><em>100 </em><em>is </em><em>not </em><em>considered </em><em>in </em><em>multiples.</em>

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